Of the 77 reported fatalities in underground coal mines nationwide from 2007-2011, 26 were a result of roof or rib falls (MSHA, 2011), and according to one report, as many as 90% of roof falls in underground mines in the Appalachian Plateau province occur in mines beneath stream valleys, yet surface topography is not commonly taken quantitatively into account when planning underground excavations (Moebs and Stateham, 1984; 1985). Roof collapse has been studied for over a century, with resulting standard practices for dealing with roof instabilities based on empirical or back-of the envelope calculations (e.g., Mucho and Mark, 1994). For practical reasons, these practices typically ignore the effects of stress perturbations due to topographic relief at the earth's surface. Pre-existing geologic structures such as faults, joints, and buried stream channels may also cause stress perturbations and/or form surfaces of weakness. Such geologic structures are frequently accounted for, although often only qualitatively or empirically. In the proposed investigation, the heterogeneous stress field induced at the scale of an individual mine by the interaction of topography and tectonic stresses will be modeled using the Boundary Element Method, with a long-range goal of developing a user-friendly software package specially designed for mining engineers to evaluate heterogeneous stress fields before and after mine excavation. Our study will focus on an active (200-500 ft. deep) coal mine in eastern Ohio which has suffered considerable ground control issues which appear to be spatially correlated with variations in surface topography. The study site, the Carroll Hollow Mine, is operated by the Sterling Mining Corporation, the underground mining subsidiary of the East Fairfield Coal Company, and work will be conducted in conjunction with PI-Griffith (Asst. Professor, Geology and Environmental Science at UA), co-PI Ernian Pan (Professor, Civil Engineering at UA), and Tim Miller, (mine geologist for East Fairfield Coal Company and the Sterling Mining Company). Our approach consists of generating a 3D model surface, made of a grid of triangular elements, which will be created from a freely available LiDAR point cloud of the topography in the vicinity of the mine. This surface will be modeled as a dislocation along which tractions are prescribed to be zero. This surface perturbs the subsurface stress field which results from a superposition of gravitational and tectonic forces. The viability of this modeled stress field will be evaluated by more detailed entry-scale models and field investigations. In these entry-scale models, the local stress tensor from the mine-scale stress field will be evaluated as it interacts with local excavation geometry, as well as mapped geologic structures. Entry-scale models will be evaluated against field examples in a mine in which roof failure has been concentrated in portions of the mine overlain by a large stream valley. In subsequent model iterations, increasing complexity (faults, excavation geometry) will be incorporated into the numerical model until the theoretical 3D stress state best matches the observed rock fall distribution. The long-range goal of this investigation is to develop an intuitive software package which mining engineers can use daily to evaluate heterogeneous stress fields before and after mine excavation. Requested funds will support students in both Geology and Civil Engineering. In addition to interacting through interdisciplinary research crossing STEM fields (Geology and Engineering), the two graduate students involved in this project will be trained in the use of Green's functions and the boundary integral equation method.